Superconducting device that mixes surface acoustic waves and microwave signals

ABSTRACT

A superconducting device that mixes surface acoustic waves and microwave signals and techniques for fabricating the same are provided. A superconducting device can comprise a superconducting surface acoustic wave resonator and a superconducting microwave resonator. The superconducting device can also comprise a Josephson ring modulator coupled to the superconducting surface acoustic wave resonator and the superconducting microwave resonator. The Josephson ring modulator can be a dispersive nonlinear three-wave mixing element.

BACKGROUND

In quantum circuits, a Josephson ring modulator is coupled to twosuperconducting microwave resonators and three-way mixing is performedbetween differential modes supported by the two superconductingmicrowave resonators and a non-resonant, common drive fed to theJosephson ring modulator. Due to coupling the Josephson ring modulatorto the two superconducting microwave resonators, the device is limitedin the choice of the frequency of differential modes, which can causeone or more problems. For example, coupling the Josephson ring modulatorto low-frequency, transmission-line resonators can have variousproblems, such as occupying a large area (e.g., a large footprint).Another problem is the relatively large linear inductance associatedwith the low resonance-frequency transmission-line compared to theinductance of the Josephson ring modulator. This can result in a veryreduced participation ratio which in turn requires, for its operation,very high external quality factors (Qs) for the resonators. However,high external Qs for the resonators is undesirable because it can giverise to very narrow dynamical bandwidths, which severely limit thedevice usability and practicality.

In addition, coupling the Josephson ring modulator to low-frequency,lumped-element resonators can require the use of large lumpedcapacitances and large lumped inductances. Large lumped capacitances andinductances are difficult to realize in practice. Large capacitances canhave considerable loss (lowering the internal Q of the device) and as aresult can cause a considerable portion of the quantum signal to belost. Large geometric inductances usually suffer from parasiticcapacitances which limit their utility. Large kinetic inductancesusually rely on unconventional thin superconductors which are difficultto fabricate and integrate.

SUMMARY

The following presents a summary to provide a basic understanding of oneor more embodiments of the invention. This summary is not intended toidentify key or critical elements, or delineate any scope of theparticular embodiments or any scope of the claims. Its sole purpose isto present concepts in a simplified form as a prelude to the moredetailed description that is presented later. In one or more embodimentsdescribed herein are devices, systems, methods, computer-implementedmethods, apparatuses, and/or computer program products that mix surfaceacoustic waves and microwave signals.

According to an embodiment, a superconducting device can comprise asuperconducting surface acoustic wave resonator and a superconductingmicrowave resonator. The superconducting device can also comprise aJosephson ring modulator coupled to the superconducting surface acousticwave resonator and the superconducting microwave resonator. TheJosephson ring modulator can be a dispersive nonlinear three-wave mixingelement. An advantage of such a superconducting device is thatdissipationless, three-wave mixing and amplification can be performedbetween low wave microwave frequencies of the superconducting surfaceacoustic wave resonator and high microwave frequencies of thesuperconducting microwave resonator.

In some examples, the superconducting surface acoustic wave resonator ofthe superconducting device can comprise a first superconducting Braggmirror and a second superconducting Bragg mirror. The secondsuperconducting Bragg mirror can be separated from the firstsuperconducting Bragg mirror by a distance that is an odd integermultiple of a half-wavelength supported by the superconducting surfaceacoustic wave resonator. An advantage of such a superconducting deviceis that the superconducting device can operate over a single, a few, ormany modes of the superconducting surface acoustic wave resonator.

According to some implementations, the superconducting device can alsoadvantageously comprise a first external feedline coupled to thesuperconducting surface acoustic wave resonator through aninterdigitated capacitance device. The first external feedline can carryone or more first input signals and one or more first output signals ofthe superconducting surface acoustic wave resonator. Further, thesuperconducting device can comprise a second external feedline coupledto the superconducting microwave resonator. The second external feedlinecan carry one or more second input signals and one or more second outputsignals of the superconducting microwave resonator. An advantage of sucha superconducting device is that low frequencies of the superconductingsurface acoustic wave resonator and high frequencies of thesuperconducting microwave resonator can be received, mixed, andamplified.

According to an embodiment, provided is a superconducting circuit thatcan comprise a superconducting surface acoustic wave resonator and aJosephson ring modulator coupled to the superconducting surface acousticwave resonator. Further, the superconducting circuit can comprise asuperconducting microwave resonator coupled to the Josephson ringmodulator. The Josephson ring modulator is a dispersive nonlinearthree-wave mixing element. According to some implementations, thesuperconducting surface acoustic wave resonator is realized on alow-loss piezo-electric dielectric substrate. An advantage of such asuperconducting circuit is that dissipationless, three-wave mixing andamplification can be facilitated between low wave microwave frequenciesof the superconducting surface acoustic wave resonator and highmicrowave frequencies of the superconducting microwave resonator.

The superconducting surface acoustic wave resonator of thesuperconducting circuit can comprise, according to some implementations,a first superconducting Bragg mirror and a second superconducting Braggmirror. The first superconducting Bragg mirror and the secondsuperconducting Bragg mirror can be separated by a distance that is anodd integer multiple of a half-wavelength supported by thesuperconducting surface acoustic wave resonator. An advantage of such asuperconducting circuit is that low frequencies of the superconductingsurface acoustic wave resonator and high frequencies of thesuperconducting microwave resonator can be received, mixed, andamplified.

In accordance with some implementations, the superconducting circuit cancomprise a first external feedline coupled to the superconductingsurface acoustic wave resonator through an interdigitated capacitancedevice. The first external feedline can carry one or more first inputsignals and one or more first output signals of the superconductingsurface acoustic wave resonator. In addition, the superconductingcircuit can comprise a second external feedline coupled to thesuperconducting microwave resonator. The second external feedline cancarry one or more second input signals and one or more second outputsignals of the superconducting microwave resonator. An advantage of sucha superconducting circuit is that low frequencies of the superconductingsurface acoustic wave resonator and high frequencies of thesuperconducting microwave resonator can be received, mixed, andamplified.

Another embodiment relates to a method that can comprise forming aJosephson ring modulator that comprises one or more Josephson junctionsarranged in a Wheatstone-bridge configuration. The method can alsocomprise coupling the Josephson ring modulator to a superconductingsurface acoustic wave resonator and a superconducting microwaveresonator. The Josephson ring modulator can be a dispersive nonlinearthree-wave mixing element. An advantage of such a method is that asuperconducting device can be fabricated, which can performdissipationless, three-wave mixing between low wave microwavefrequencies of the superconducting surface acoustic wave resonator andhigh microwave frequencies of the superconducting microwave resonator.

In some implementations, the method can comprise forming thesuperconducting surface acoustic wave resonator from a firstsuperconducting Bragg mirror and a second superconducting Bragg mirror.The method can also comprise separating the first superconducting Braggmirror from the second superconducting Bragg mirror by a distancedefined as an odd integer multiple of a half-wavelength supported by thesuperconducting surface acoustic wave resonator. An advantage of such amethod is that the fabricated superconducting device can operate over asingle, a few, or many modes of the superconducting surface acousticwave resonator

A further embodiment relates to a superconducting device that cancomprise a superconducting surface acoustic wave resonator. Thesuperconducting surface acoustic wave resonator can comprise a firstperiodic structure comprising first metallic fingers and firstdielectric gaps. The superconducting surface acoustic wave resonator canalso comprise a second periodic structure comprising second metallicfingers and second dielectric gaps. The first periodic structure and thesecond periodic structure can be separated by a distance defined as anodd integer multiple of a half-wavelength supported by thesuperconducting surface acoustic wave resonator. Further, thesuperconducting device can comprise a dispersive nonlinear three-wavemixing element coupled to the superconducting surface acoustic waveresonator. The dispersive nonlinear three-wave mixing element cancomprise one or more Josephson junctions arranged in a Wheatstone-bridgeconfiguration. In addition, the superconducting device can comprise asuperconducting microwave resonator coupled to the dispersive nonlinearthree-wave mixing element. An advantage of such a superconducting deviceis that dissipationless, three-wave mixing and amplification can beperformed between low wave microwave frequencies of the superconductingsurface acoustic wave resonator and high microwave frequencies of thesuperconducting microwave resonator while occupying a small space andthrough the use of low-loss resonators.

DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example, non-limiting block diagram of a circuitcomprising the Josephson ring modulator in accordance with one or moreembodiments described herein.

FIG. 2 illustrates an example, non-limiting block diagram of a circuitcomprising a superconducting surface acoustic wave resonator inaccordance with one or more embodiments described herein.

FIG. 3 illustrates an example, non-limiting, schematic of a circuit fora superconducting device that comprises a surface acoustic waveresonator and superconducting microwave resonator coupled to a Josephsonring modulator in accordance with one or more embodiments describedherein.

FIG. 4 illustrates a flow diagram of an example, non-limiting, methodfor fabrication of a device in accordance with one or more embodimentsdescribed herein.

FIG. 5 illustrates a flow diagram of an example, non-limiting, methodfor fabrication of a device comprising a pump drive port in accordancewith one or more embodiments described herein.

FIG. 6 illustrates a flow diagram of an example, non-limiting, methodfor fabrication of a device comprising two metallic/dielectric mirrorsin accordance with one or more embodiments described herein.

FIG. 7 illustrates a flow diagram of an example, non-limiting, methodfor fabrication of a device comprising a Josephson ring modulatorcoupled to a superconducting surface acoustic wave resonator and asuperconducting microwave resonator in accordance with one or moreembodiments described herein.

FIG. 8 illustrates a flow diagram of an example, non-limiting, methodfor fabrication of a superconducting quantum device in accordance withone or more embodiments described herein.

FIG. 9 illustrates a flow diagram of an example, non-limiting, methodfor fabrication of a superconducting quantum device comprising externalfeedlines in accordance with one or more embodiments described herein.

FIG. 10 illustrates a block diagram of an example, non-limitingoperating environment in which one or more embodiments described hereincan be facilitated.

DETAILED DESCRIPTION

The following detailed description is merely illustrative and is notintended to limit embodiments and/or application or uses of embodiments.Furthermore, there is no intention to be bound by any expressed orimplied information presented in the preceding Background or Summarysections, or in the Detailed Description section.

One or more embodiments are now described with reference to thedrawings, wherein like referenced numerals are used to refer to likeelements throughout. In the following description, for purposes ofexplanation, numerous specific details are set forth in order to providea more thorough understanding of the one or more embodiments. It isevident, however, in various cases, that the one or more embodiments canbe practiced without these specific details.

As it relates to circuits, and more specifically quantum circuits, if aJosephson ring modulator (JRM) is coupled to two superconducting waveresonators, there is a limitation with respect to the choice of thedifferential modes that couple to the JRM. For example, a problemassociated with coupling the JRM to low-frequency, transmission-lineresonators is that a large area is occupied by the device. A solutionprovided by the superconducting device, the superconducting circuit, andthe methods discussed herein is that a superconducting surface acousticwave resonator is utilized, which is compact and, therefore, a size ofthe superconducting device is reduced.

Another problem associated with prior art superconducting devices (e.g.,devices that utilize two superconducting microwave resonators) is thatthe prior art superconducting devices are limited to mixing frequenciesbetween 5 Gigahertz (GHz) and 15 GHz. The various superconductingdevices, circuits, and methods discussed herein provide a solution tothis problem through the utilization of a superconducting surfaceacoustic wave resonator and superconducting wave resonator that enabledissipationless, three-wave mixing and amplification between lowmicrowave frequencies (e.g., about 0.1 GHz to about 4 GHz) and highmicrowave frequencies (e.g., around 5 GHz to around 15 GHz).

Given the above problems with prior art superconducting devices, thevarious aspects provided herein can be implemented to produce a solutionto one or more of these problems in the form of a superconductingdevice, superconducting circuit, and method of fabricating the same.Such systems, devices, circuits, methods, computer-implemented methods,and/or computer program products implementing such a superconductingdevice can have an advantage of reduced size and low-loss resonators, ascompared to conventional techniques.

According to some implementations, the device can function as aJosephson mixer between surface acoustic waves (phonons) and microwavesignals (photons). Additionally, or alternatively, the device canfunction as a lossless frequency converter between a surface acousticwave and a microwave signal. Additionally, or alternatively, the devicecan function as a nondegenerate parametric Josephson amplifier for asurface acoustic wave and a microwave signal. In additional oralternative implementations, the device can function as an entangler ofa phononic mode and photonic mode.

FIG. 1 illustrates an example, non-limiting block diagram of a circuit100 in accordance with one or more embodiments described herein. Thecircuit 100 can comprise a superconducting surface acoustic wave (SAW)resonator (referred to as a superconducting SAW resonator 102), asuperconducting microwave resonator 104, and a Josephson ring modulator(referred to as a JRM 106).

In a piece of quantum hardware, which includes the superconductingqubits space, a mechanism to implement gate operations or measurementson the quantum hardware is to generate microwave signals or receivemicrowave signals by the superconducting SAW resonator 102 and/or viathe superconducting microwave resonator 104. As discussed herein,according to some implementations, the circuit 100 can operate as aJosephson mixer between surface acoustic waves (phonons) and microwavesignals (photons). Further, the circuit 100 can operate as a losslessfrequency converter between a surface acoustic wave and a microwavesignal. In some implementations, the circuit 100 can operate as anondegenerate parametric Josephson amplifier for a surface acoustic waveand a microwave signal. In additional and/or alternate implementations,the device can operate as an entangler of a phononic mode and photonicmode.

SAW resonators (e.g., the superconducting SAW resonator 102) areelectro-mechanical resonators for phonons, which can resonate atmicrowave frequencies of around 0.5 GHz to 5 GHz. Surface acoustic waveresonators (or surface acoustic wave filters) are used in manytelecommunication applications (e.g., mobile phones). SAW resonators canalso be useful in quantum computing applications and quantum circuits inthe microwave domain, as discussed herein. Further, surface acousticwave resonators can have high internal Quality (Q) factors, which can bein excess of 10⁵. Therefore, SAW resonators can have a very low loss. Inaddition, SAW resonators are very compact. For example, the surfaceacoustic resonance wavelengths are very short (e.g., less than 1 micrometre or <1 μm).

The superconducting SAW resonator 102 can be a low frequency device andthe superconducting microwave resonator 104 can be a high frequencydevice. Further, the superconducting SAW resonator 102 can beimplemented on a low-loss piezo-electric dielectric substrate. Thelow-loss piezo-electric dielectric substrate can comprise a materialselected from a group of materials comprising quartz, gallium arsenide,lithium niobite, and/or zinc oxide, or the like. The superconductingmicrowave resonator 104 can be implemented using lumped-elementcapacitance and lumped-element inductance. Further details related tothe superconducting SAW resonator 102 and the superconducting microwaveresonator 104 will be provided below with respect to FIGS. 2 and 3.

The JRM 106 is a device that can be based on Josephson tunnel junctions.For example, the JRM 106 can comprise one or more Josephson junctionsarranged in a Wheatstone-bridge configuration. The one or more Josephsonjunctions can comprise a material selected from a group of materialscomprising aluminum and niobium. Further, the JRM 106 can performnon-degenerate mixing in the microwave regime, without losses. Accordingto some implementations, the JRM 106 can be a dispersive nonlinearthree-wave mixing element.

The JRM 106 can support two differential modes and two common modes (oneof which is at zero frequency, and, therefore, not applicable to the oneor more embodiments described herein). By coupling the JRM 106 to asuitable electromagnetic environment (which supports two differentialmicrowave modes), the circuit 100 can be used to perform various quantumprocessing operations such as lossless frequency conversion in themicrowave domain, parametric amplification at the quantum limit (e.g.,amplification of quantum signals in the microwave domain), and/orgeneration of two-mode squeezing.

The Josephson ring modulator (e.g., the JRM 106) can comprise one ormore Josephson junctions arranged in a Wheatstone-bridge configuration.The Josephson junctions are illustrated as a first Josephson junction108, a second Josephson junction 110, a third Josephson junction 112,and a fourth Josephson junction 114. The Josephson junctions (e.g., thefirst Josephson junction 108, the second Josephson junction 110, thethird Josephson junction 112, the fourth Josephson junction 114) can beformed in a loop. Further, the Josephson junctions can be utilized toperform the mixing as discussed herein.

The JRM 106 also can comprise four additional junctions (internal to theloop), which can be shunt junctions according to some implementations.These four additional junctions are labeled as a first internal junction116, a second internal junction 118, a third internal junction 120, anda fourth internal junction 122. The four internal junctions (e.g., thefirst internal junction 116, the second internal junction 118, the thirdinternal junction 120, and the fourth internal junction 122) canfacilitate tuning of the frequency of the circuit 100. The tunabilitycan be obtained with the application of external magnetic flux. Forexample, induced magnetic flux threads the Josephson ring modulator. Inthis configuration, the four internal junctions, which are larger thanthe junctions on the outer loop, can function as linear inductorsshunting the outer Josephson junctions. By threading external fluxthrough the inner loops, the total inductance of the JRM 106 can change,which can lead to a change in the resonance frequencies of the resonatorcoupled to the JRM 106. According to some implementations, threading theexternal flux can be facilitated with magnetic coils, on-chip fluxlines, nearby flux lines, and/or on a different chip/layer.

In addition, the configuration of the JRM 106 defines points or nodeswhere the external junctions meet. Accordingly, there can be a firstnode 124 at the bottom of the JRM 106; a second node 126 at the rightside of the JRM 106; a third node 128 at the top of the JRM 106; and afourth node 130 at the left side of the JRM 106. It is noted that theterms bottom, right side, top, and left side are for purposes ofexplaining the disclosed aspects with respect to the figures and thedisclosed aspects are not limited to any particular plane or orientationof the JRM 106 and/or the circuit 100 and its associated circuitry.

The four nodes (e.g., the first node 124, the second node 126, the thirdnode 128, and the fourth node 130) can be utilized to define thedifferential mode and the common mode hosted by the circuit 100. Themodes can be orthogonal and do not overlap one another. Further, thenodes, as illustrated, can be physically orthogonal. For example, thefirst node 124 and the third node 128 are vertical to one another andthe second node 126 and the fourth node 130 are horizontal to oneanother.

The nodes can be utilized to couple the JRM 106 to the superconductingSAW resonator 102 and to the superconducting microwave resonator 104.For example, a first set of opposite nodes (e.g., the first node 124 andthe third node 128) can be chosen to operatively couple the JRM 106 tothe superconducting SAW resonator 102. The first node 124 can be coupledto the superconducting SAW resonator 102 via a first wire 132 (or firstlead) and the third node 128 can be coupled to the superconducting SAWresonator 102 via a second wire 134 (or second lead).

The second set of opposite nodes (e.g., the second node 126 and thefourth node 130) can be chosen to operatively couple the JRM 106 to thesuperconducting microwave resonator 104. For example, the second node126 can be coupled to the superconducting microwave resonator 104 via athird wire 136 (or third lead) and the fourth node 130 can be coupled tothe superconducting microwave resonator 104 via a fourth wire 138 (orfourth lead).

As illustrated, the first wire 132 and the second wire 134 can becoupled to the superconducting SAW resonator 102 at different locationsof the superconducting SAW resonator 102. Further, the third wire 136and the fourth wire 138 can be coupled to the superconducting microwaveresonator 104 at different locations of the superconducting microwaveresonator 104. Further details related to the coupling locations will beprovided below with respect to FIG. 3.

The superconducting SAW resonator 102, the superconducting microwaveresonator 104, and the JRM 106 are portions of afrequency-converter/mixer/amplifier/entangler device. The device canreceive external microwave photons or phonons from other quantum devicesconnected to the microwave port and/or the SAW port of the device.

The circuit 100, as well as other aspects discussed herein can beutilized in a device that facilitates manipulation of quantuminformation in accordance with one or more embodiments described herein.Aspects of devices (e.g., the circuit 100 and the like), systems,apparatuses, or processes explained in this disclosure can constitutemachine-executable component(s) embodied within machine(s), e.g.,embodied in one or more computer readable mediums (or media) associatedwith one or more machines. Such component(s), when executed by the oneor more machines, e.g., computer(s), computing device(s), virtualmachine(s), etc. can cause the machine(s) to perform the operationsdescribed.

In various embodiments, the device can be any type of component,machine, system, device, facility, apparatus, and/or instrument thatcomprises a processor and/or can be capable of effective and/oroperative communication with a wired and/or wireless network.Components, machines, apparatuses, systems, devices, facilities, and/orinstrumentalities that can comprise the device can include tabletcomputing devices, handheld devices, server class computing machinesand/or databases, laptop computers, notebook computers, desktopcomputers, cell phones, smart phones, consumer appliances and/orinstrumentation, industrial and/or commercial devices, hand-helddevices, digital assistants, multimedia Internet enabled phones,multimedia players, and the like.

In various embodiments, the device can be a quantum computing device orquantum computing system associated with technologies such as, but notlimited to, quantum circuit technologies, quantum processortechnologies, quantum computing technologies, artificial intelligencetechnologies, medicine and materials technologies, supply chain andlogistics technologies, financial services technologies, and/or otherdigital technologies. The circuit 100 can employ hardware and/orsoftware to solve problems that are highly technical in nature, that arenot abstract and that cannot be performed as a set of mental acts by ahuman. Further, in certain embodiments, some of the processes performedcan be performed by one or more specialized computers (e.g., one or morespecialized processing units, a specialized computer with a quantumcomputing component, etc.) to carry out defined tasks related to machinelearning.

The device and/or components of the device can be employed to solve newproblems that arise through advancements in technologies mentionedabove, computer architecture, and/or the like. One or more embodimentsof the device can provide technical improvements to quantum computingsystems, quantum circuit systems, quantum processor systems, artificialintelligence systems and/or other systems. One or more embodiments ofthe circuit 100 can also provide technical improvements to a quantumprocessor (e.g., a superconducting quantum processor) by improvingprocessing performance of the quantum processor, improving processingefficiency of the quantum processor, improving processingcharacteristics of the quantum processor, improving timingcharacteristics of the quantum processor, and/or improving powerefficiency of the quantum processor.

FIG. 2 illustrates an example, non-limiting block diagram of a circuit200 comprising a superconducting surface acoustic wave (SAW) resonatorin accordance with one or more embodiments described herein. Repetitivedescription of like elements employed in other embodiments describedherein is omitted for sake of brevity.

The superconducting SAW resonator 102 can comprise a firstsuperconducting metallic/dielectric mirror (e.g., a first Bragg mirror202) and a second superconducting metallic/dielectric mirror (e.g., asecond Bragg mirror 204). The first Bragg mirror 202 can be separatedfrom the second Bragg mirror 204 by a distance that is an odd integermultiple of a half-wavelength supported by the superconducting SAWresonator 102. A Bragg mirror comprises a periodic structure of metallicfingers and dielectric gaps positioned at a defined distance from oneanother.

According to some implementations, the superconducting SAW resonator 102can be attached to (e.g., realized on) a low-loss piezo-electricdielectric substrate (not shown). The low-loss piezo-electric dielectricsubstrate can comprise a material selected from a group of materialscomprising one or more of quartz, gallium arsenide, lithium niobite, andzinc oxide, or a similar material.

Further, a first interdigitated capacitance device or first IDC device206 and a second IDC device 208 can be included. The first IDC device206 can couple between the superconducting SAW resonator 102 and the JRM106. The second IDC device 208 can couple between the superconductingSAW resonator 102 and an external port (e.g., a signal port 212).

For example, the first IDC device 206 can be positioned at a center ofthe superconducting SAW resonator 102. A first set of opposite nodes ofthe JRM 106 can be connected to opposite nodes of the first IDC device206. For example, the first node 124 of the JRM 106 can be connected toa first side of the first IDC device 206 (e.g., via the first wire 132).Further, the third node 128 of the JRM 106 can be connected to a secondside of the first IDC device 206 (e.g., via the second wire 134).

A second set of opposite nodes of the Josephson ring modulator can beconnected to the superconducting microwave resonator 104. For example,the second node 126 of the JRM 106 can be connected to a first side ofthe superconducting microwave resonator 104 (e.g., via the third wire136). Further, the fourth node 130 of the JRM 106 can be connected to asecond side of the superconducting microwave resonator 104 (e.g., viathe fourth wire 138).

The circuit 100 can also comprise a first external feedline 210 coupledto the superconducting SAW resonator 102 through the second IDC device208. The first external feedline 210 can be connected to a signal port212 (e.g., a radio frequency (rf) source). The first external feedline210 can carry one or more input signals and one or more output signalsof the superconducting SAW resonator 102.

A second external feedline 214 can be coupled to the superconductingmicrowave resonator 104. The second external feedline 214 can beconnected to an idler port 216 (e.g., a microwave source). The secondexternal feedline 214 can carry one or more input signals and one ormore output signals of the superconducting microwave resonator 104.

Further, the JRM 106 can be operative connected to a pump port 218(e.g., via the second wire 134 or another wire). The pump port 218 canbe connect to a microwave source. The pump port 218 can supply therequired energy for the operation of the circuit 100. For example, uponor after pump power is supplied from the pump port 218 to the JRM 106,the superconducting SAW resonator 102 and the superconducting microwaveresonator 104 can be electrically connected through the JRM 106.However, when power is not supplied through the pump port 218 (e.g., thepower supply is off), the superconducting SAW resonator 102 and thesuperconducting microwave resonator 104 can be electrically isolatedfrom one another.

For amplification, ideally there would be a microwave signal that ispropagating on the idler transmission line (e.g., the second externalfeedline 214) that is connected to the idler port 216. In an example,assume that the microwave signal is weak and it carries some quantuminformation that is of value. The information goes into the circuit 100and there is a pump tone that is fed to the device (e.g., via the pumpport 218) that can generate a parametric amplification between the idlermode and the signal mode supported by the superconducting SAW resonator102. In this example, an input signal is not needed at both the signalport 212 and the idler port 216. Instead, a signal is only needed on oneport and quantum noise can enter through the other port. Thedeterministic signal carrying quantum information and the quantum noisecan be mixed by the device via the pump drive and amplified upon leavingthe device. Thus, the signal that carries information can come eitherfrom the signal port 212, or the idler port 216, or can have two signalscarrying information entering both ports at substantially the same time.For simplicity, assume the signal is entering the circuit 100 throughone port and the other port is only receiving quantum noise. In thiscase, through the interaction with the pump (e.g., the pump port 218)and the JRM 106 three-wave mixing takes place between the common mode(pump) and two differential modes (the idler and the signal). If thepump frequency is the sum of the signal and idler resonance frequencies,the device functions as a phase-preserving parametric amplifieroperating near the quantum limit. The respective output signal exitingthe signal port 212 and idler port 216 can be an amplified superpositionof the input signals entering both ports (e.g., the signal port 212 andidler port 216).

According to some implementations, magnetic flux threading the JRM 106can be induced through the one or more external superconducting magneticcoils. For example, magnetic flux threading the JRM 106 can be inducedusing external superconducting magnetic coils attached to a devicepackage or using on-chip flux lines.

In further detail, FIG. 3 illustrates an example, non-limiting,schematic of a circuit 300 for a superconducting device that comprises asurface acoustic wave resonator and superconducting microwave resonatorcoupled to a Josephson ring modulator in accordance with one or moreembodiments described herein. Repetitive description of like elementsemployed in other embodiments described herein is omitted for sake ofbrevity.

It is noted that the Josephson junctions and the four internal junctionsof the JRM 106 are not labeled in FIG. 3 for purposes of simplicity.However, the element numbering of the junctions for purposes ofexplanation are the same as the labeling of FIGS. 1 and 2. In addition,the circuit 300 and its associated components can be implemented on asingle chip, according to some implementations.

As mentioned, the nodes of the JRM 106 can comprise a first set ofopposite nodes that can be oriented in a vertical direction to oneanother. For example, the first set of opposite nodes can comprise thefirst node 124 and the third node 128, which can operatively couple theJRM 106 to the superconducting SAW resonator 102 (e.g., via the firstwire 132 and the second wire 134). Further, the nodes of the JRM 106 cancomprise a second set of opposite nodes, which can be oriented in ahorizontal manner. For example, the second set of opposite nodes cancomprise the second node 126 and the fourth node 130, which canoperatively couple the JRM 106 to the superconducting microwaveresonator 104. It is noted that although illustrated and described withrespect to a horizontal direction and/or a vertical direction, thedisclosed aspects are not limited to this orientation and otherorientations can be utilized.

The first set of opposite nodes (e.g., the first node 124 and the thirdnode 128) can be coupled to opposite electrodes of a firstinterdigitated capacitor or first IDC 302 (e.g., the first IDC device206) of the superconducting SAW resonator 102, creating a firstorthogonal mode. For example, the first node 124 of the JRM 106 can becoupled to a first electrode of the first IDC 302, indicated at 304.Further, the third node 128 of the JRM 106 can be coupled to a secondelectrode of the first IDC 302, indicated at 306. The first IDC 302 canbe positioned at a center of the superconducting SAW resonator 102.

The second set of opposite nodes (e.g., the second node 126 and thefourth node 130) can be coupled to a second capacitor 310 (e.g., ashunting capacitor) forming a superconducting microwave resonator 104,where the JRM is the inductive element of the resonator. Thesuperconducting microwave resonator can support a second orthogonaldifferential mode of the JRM 106. The capacitance (e.g., the firstcapacitor 308) functions as a coupling capacitor between the microwaveresonator (formed by the JRM 106 and the second capacitor 310) and theexternal feedline/port (e.g., the idler port 216) of the device.According to some implementations, the first capacitor 308 and thesecond capacitor 310 can be respective capacitors chosen from a group ofcapacitors comprising a gap capacitor, an interdigitated capacitor,and/or a plate capacitor. In the case of plate capacitance, thedielectric material should have very low-loss at the level of singlemicrowave photons.

As illustrated, the superconducting SAW resonator 102 can comprise thefirst IDC 302, a second IDC 312 (e.g., the second IDC device 208), and aset of metallic/dielectric mirrors (e.g., the first Bragg mirror 202 andthe second Bragg mirror 204). The components of the superconducting SAWresonator 102 (e.g., the first IDC 302, the second IDC 312, the firstBragg mirror 202, the second Bragg mirror 204) is implemented on apiezo-electric substrate. For example, the piezo electric substrate cancomprise one or more of quartz, gallium arsenide, lithium niobite, zincoxide, and/or similar materials.

Different ports can be utilized to access the superconducting SAWresonator 102 and the superconducting microwave resonator 104. Forexample, the signal port 212 can be utilized to access thesuperconducting SAW resonator 102 and the idler port 216 can be utilizedto access the superconducting microwave resonator 104.

The signal port 212 can be utilized to carry input signals and outputsignals. Therefore, in order to measure output signals from thesuperconducting SAW resonator 102, an IDC (e.g., the second IDC 312) canbe placed between the first Bragg mirror 202 and the second Bragg mirror204. One set of IDC fingers that are connected together are located atan rf-voltage anti-node (maximum/minimum) of the supported phononicmode. Therefore, the spacing between the fingers can be determined bythe wavelength supported by the superconducting SAW resonator 102.

A distance between the centers of two consecutive fingers of the IDCs(e.g., the first IDC 302 and the second IDC 312) can be generallyexpressed as λ_(a)/2. The respective two sets of fingers of the IDCs canhave opposite polarity according to an implementation. Further, thefirst Bragg mirror 202 and the second Bragg mirror 204 can be separatedfrom one other, as indicated by line 314, by a distance that is an oddinteger multiple of half-wavelength supported by the superconducting SAWresonator 102. The defined distance can be expressed as L_(a), whereinL_(a) is an odd-integer multiple of λ_(a)/2. Where λ_(b)<λ_(a).

A microwave tone is characterized by a wave that has a maximum amplitudeand a minimum amplitude. The minimum amplitude should couple to onefinger of the IDC (e.g., indicated at 304 or 306) and the maximum valueshould couple to the other finger, (e.g., indicated at 304 or 306) wherethe two fingers are connected to opposite nodes of the JRM 106 (e.g.,the first node 124 and the third node 128). Therefore, the distanceλ_(a)/2 can be selected to facilitate the maximum on the first fingerand the minimum on the other finger.

Further, for purposes of explanation, the maximum amplitude has a plussign (or a positive value) and the minimum amplitude has a minus sign(or a negative value). Therefore, the two opposite nodes of the JRM 106can be excited by the positive (on the first finger) and the negativerf-voltages (on the second finger). These signals can alternate withtime. However, they should be opposite to one another at any given time.When the polarity is different, it can be referred to as a differentialmode (where differential means opposite sign).

This can also apply to the case of the superconducting microwaveresonator 104. As mentioned, the superconducting microwave resonator cancomprise a first capacitor 308 coupling the resonator to the externalport (e.g., the idler port 216) and the second capacitor 310 shuntingthe JRM 106. The two electrodes of the capacitor shunting the JRM 106(e.g., the second capacitor 310) can have opposite voltages and canexcite a second differential mode. Accordingly, a first differentialmode of the JRM 106 is supported by the superconducting SAW resonator102 and a second differential mode of the JRM 106 is supported by thesuperconducting microwave resonator 104.

Further, in order to perform the mixing, or the amplification, microwaveenergy is supplied for device operation. The energy source for themixing and/or amplification is supplied through the pump port 218. Thepump port 218 can provide a microwave signal, which can be a strong,coherent, non-resonant microwave tone that can supply energy for thecircuit 100 to operate. According to some implementations, the microwavesignal supplied by the pump port 218 can comprise a frequency thatsatisfies a defined equation determined based on the energy conservationof the three-wave mixing occurring in the circuit 100.

In an example of amplification performed by the device, a first signalf_(a) which lies within the bandwidth of the superconducting SAWresonator 102 and a second signal f_(b) which lies within the bandwidthof the superconducting microwave resonator 104. Further, the frequencyof the second signal can be larger than the frequency of the firstsignal (f_(b)>f_(a)). To amplify both signals, the frequency of the pumptone fed through the pump port 218 should be the sum of the first signaland the second signal (e.g., f_(a)+f_(b)). The energy of theelectromagnetic signal is proportional to its frequency. By taking thepump (e.g., the pump port 218) frequency to be the sum, if the pumpinteracts with the dispersive nonlinear medium (e.g., the JRM 106), adownconversion process can occur where the energetic photons of the pumpsplit into a first set of photons at f_(a) and a second set of photonsat f_(b). If the frequency is the sum, then the photons can split inthis manner. For example, the photons can split into two halves: a firsthalf (e.g., the first set of photons) at the lower frequency f_(a) and asecond half (e.g., the second set of photons) at the higher frequencyf_(b). Therefore, amplification can occur because the pump exchangesenergy with the signal mode and idler mode and through this exchangeentangled photons are generated in both modes. Similarly, a conversionprocess with non phonon-photon gain can convert one mode to the other(e.g., a photon to a phonon or a phonon to a photon). In this case, thepump frequency should be equal to the difference between f_(a) andf_(b). Here f_(b) is larger, so the equation can be f_(b) minus f_(a).

According to an implementation, in the mixing process (conversionwithout photon-phonon gain) a phonon in the SAW resonator at the signalfrequency can be upconverted into a microwave photon in the microwaveresonator at the idler frequency. According to another implementation,the photon in the microwave resonator at the idler frequency can bedownconverted to a phonon in the SAW resonator at the signal frequency.The energy exchange is enabled by the pump drive (e.g., fed through thepump port 218). Accordingly, either a pump photon is emitted or a pumpphoton is absorbed to facilitate the process.

If there is no pump signal applied to the pump port 218, thesuperconducting SAW resonator 102 and the superconducting microwaveresonator 104 are separated (e.g., isolated from one another) andinformation exchange or information communications between thesuperconducting SAW resonator 102 and the superconducting microwaveresonator 104 does not occur. Upon or after a pump signal is applied tothe pump port 218, it excites the common mode of the JRM 106, asillustrated in FIG. 2, the superconducting SAW resonator 102 and thesuperconducting microwave resonator 104 interact and information isexchanged.

According to some implementations, the pump drive is fed through thesigma port of a 180-degree hybrid 316, which is capacitively coupled toopposite nodes of the JRM 106, which in turn excites a common-mode ofthe JRM 106. According to some implementations, the 180-degree hybrid316 operates as a power splitter.

By way of explanation and not limitation, a 180-degree hybrid is apassive microwave component that comprises four ports. A first port isreferred to as a sum port 318 (or sigma port). If a signal is input tothe sum port 318, the signal splits equally between two other ports(e.g., a second port 320 and a third port 322). The signals that areoutput from the second port 320 and the third port 322 can have the samephase. Thus, the first port is referred to as the sum port 318 becausethe phases of the split signals are equal. The pump drive (e.g., thepump port 218) can be fed through the sum port 318 of the 180-degreehybrid 316.

A fourth port can be referred to as a delta port 324 (or a differenceport). If a signal is injected through the delta port 324 of the180-degree hybrid (which, in FIG. 3, is terminated with 50 ohms), thehybrid would split the signal into two signals, coming out of the twoports (e.g., the second port 320 and the third port 322), but the splitsignals have a 180-degree phase difference. For example, if a firstsignal has a maximum value at one port (e.g., 320), the second signal atthe other port (e.g., 322) has a minimum value. The pump port 218 can befed through the sum port 318.

Also illustrated are a first lead 326 coming out of the second port 320and a second lead 328 coming out of the third port 322. The signals thatare output at the second port 320 and the third port 322 are half of thepump signal and have the same phase, as discussed above. The signalsencounter small coupling capacitors (e.g., a first coupling capacitor330 and a second coupling capacitor 332) that can be coupled to twoopposite nodes of the JRM 106. According to some implementations, thefirst coupling capacitor 330 and the second coupling capacitor 332 canbe respective capacitors chosen from a group of capacitors comprising agap capacitor, an interdigitated capacitor, and a plate capacitor. As itrelates to plate capacitance, the dielectric material should have verylow-loss at the level of single microwave photons.

The first coupling capacitor 330 can be coupled to the first node 124 ofthe JRM 106 (through the first IDC 302) and the second couplingcapacitor 332 can be coupled to the third node 128 of the JRM 106. Infurther detail, the first lead 326 and the second lead 328 can couple totwo different sets of fingers of the first IDC 302 (illustrated at thefirst contact point 306 and a third contact point 334), that couple totwo opposite nodes of the JRM 106. This connection enables exciting thecommon mode of the JRM 106 where the two opposite nodes of the JRM 106are excited, not with opposite rf-voltage signs, but with equal signs.For example, the two opposite nodes can be excited with apositive-positive signal or a negative-negative signal.

The first lead 326 and the second lead 328 can be connectingsuperconducting wires that should be equal in length (e.g., phasematched) between the ports (e.g., the second port 320, the third port322) of the 180 degree hybrid and the coupling capacitors (e.g., thefirst coupling capacitor 330, the second coupling capacitor 332,respectively). Also, the first wire 132 and the second wire 134 can beconnecting superconducting wires that should be equal in length (e.g.,phase matched) between the opposite nodes of the JRM 106 and theelectrodes of the first IDC 302. Also, the third wire 136 and the fourthwire 138 can be connecting superconducting wires that should be equal inlength (e.g., phase matched) between the opposite nodes of the JRM 106and the electrodes of the second capacitor 310. Further, the connectingsuperconducting wires should be as short as possible and wide (e.g.,have small series inductance).

The following provides further technical comments for an understandingof the various aspects disclosed herein. The speed of sound in thevarious piezoelectric substrates can be slower than the speed of lightby several orders of magnitude (e.g., approximately five orders ofmagnitude, for example, 10⁵).

The effective length of the superconducting SAW resonator 102 can beslightly larger than L_(a). This can be because the reflection off theBragg mirrors does not happen on the mirror edges but within a certainpenetration depth inside the Bragg mirrors.

The effective length (L_(eff)) of the superconducting SAW resonator 102and the speed of sound in the piezoelectric substrate (v_(s)) candetermine the cavity free spectral range (FSR):

$V_{FSR} = {\frac{v_{s}}{2L_{eff}}.}$The SAW resonator can be similar to photonic cavities that supportmultimodes (resonances). The cavity free spectral range parameter candetermine the frequency spacing between the multimodes supported by thesuperconducting SAW resonator 102.

The larger the spacing between the Bragg mirrors, the larger L_(eff) is,and as a result the smaller the frequency separation between the SAWresonator modes. The Bragg mirrors can operate as reflective mirrorswithin a certain bandwidth. Modes that fall beyond their bandwidth arenot supported by the SAW resonator because their phononic modes are notconfined.

Depending on the V_(FSR) and the bandwidth of the Bragg mirrors, thecircuit 100 can operate over a single, a few, or many modes of the SAWresonator. It is noted that not all the modes supported by the SAWresonator would strongly couple to the JRM. Three-wave mixing operationsin the circuit 100 can take place with phononic modes that couplestrongly to the JRM. Modes couple strongly to the JRM when theiranti-nodes align with the IDC fingers coupled to the JRM.

The circuit 100 can be a three-wave mixer, such as a Josephson mixerthat relies on non-linear inductance of the Josephson junctions, whichis lossless. The Josephson mixer is used to allow mixing between phononssupported by the superconducting SAW resonator 102 and microwavesignals, which are carried by photons. This is different fromconventional devices that couple a phonon to a phonon or a photon to aphoton. Therefore, the disclosed aspects provide a significantimprovement in the coupling. For example, the circuit 100 can allowconversion from a microwave signal to acoustic waves that resonate atlow microwave frequencies. Further, the circuit 100 can amplify in anondegenerate manner Nondegenerate here means: (1) the circuit 100 isamplifying two different frequencies: one frequency at a high microwavefrequency (example 12 GHz) and another relatively low microwavefrequency (example 1 GHz), thus, nondegenerate means that thefrequencies are different so there is a spectral nondegeneracy; and (2)there is also a spatial nondegeneracy because the microwave signal issupported by the superconducting microwave resonator 104, which isphysically different than the superconducting SAW resonator 102 thatsupports the surface acoustic wave. Therefore, there is a spectral and aphysical nondegeneracy. Due to this process of parametric amplificationthat is nondegenerate, the circuit 100 can entangle a phononic mode witha photonic mode, where entanglement is a quantum property where the twomodes are strongly correlated with one another and inseparable from oneanother. Therefore, if a measurement is taken of one, the state of theother can be determined. Thus, they are entangled and they form oneentity, although they can be separated in space by distance.

FIG. 4 illustrates a flow diagram of an example, non-limiting, method400 for fabrication of a device in accordance with one or moreembodiments described herein. Repetitive description of like elementsemployed in other embodiments described herein is omitted for sake ofbrevity.

At 402 of the method 400, a Josephson ring modulator (e.g., the JRM 106)can be formed. The Josephson ring modulator can comprise one or moreJosephson junctions (e.g., the first Josephson junction 108, the secondJosephson junction 110, the third Josephson junction 112, the fourthJosephson junction 114) arranged in a Wheatstone-bridge configuration.The one or more Josephson junctions can comprise a first materialselected from a first group of materials comprising aluminum andniobium.

Further, at 404 of the method 400, the Josephson ring modulator can becoupled to a superconducting surface acoustic wave resonator (e.g., thesuperconducting SAW resonator 102) and a superconducting microwaveresonator (e.g., the superconducting microwave resonator 104). TheJosephson ring modulator can be a dispersive nonlinear three-wave mixingelement.

FIG. 5 illustrates a flow diagram of an example, non-limiting, method500 for fabrication of a device comprising a pump drive port inaccordance with one or more embodiments described herein. Repetitivedescription of like elements employed in other embodiments describedherein is omitted for sake of brevity.

The method 500 starts at 502, when a Josephson ring modulator (e.g., theJRM 106) is formed. The Josephson ring modulator can comprise one ormore Josephson junctions (e.g., the first Josephson junction 108, thesecond Josephson junction 110, the third Josephson junction 112, thefourth Josephson junction 114) arranged in a Wheatstone-bridgeconfiguration. Further, the Josephson ring modulator can comprise aport, through which a pump drive (e.g., the pump port 218) can be fed.

At 504 of the method 500, a superconducting surface acoustic waveresonator (e.g., the superconducting SAW resonator 102) can be formed.The superconducting surface acoustic wave resonator can be realized on apiezoelectric substrate. A superconducting microwave resonator (e.g.,the superconducting microwave resonator 104) can be formed at 506.Further, at 508, the Josephson ring modulator can be coupled to thesuperconducting surface acoustic wave resonator and the superconductingmicrowave resonator.

A pump drive can be injected to the Josephson ring modulator through theport, at 510 of the method 500. For example, the pump drive can be fedthrough a sigma port of a 180-degree hybrid (e.g., the 180-degree hybrid316). The 180-degree hybrid can be capacitively coupled to oppositenodes of the Josephson ring modulator, which in turn excites acommon-mode of the Josephson ring modulator.

FIG. 6 illustrates a flow diagram of an example, non-limiting, method600 for fabrication of a device comprising two metallic/dielectricmirrors in accordance with one or more embodiments described herein.Repetitive description of like elements employed in other embodimentsdescribed herein is omitted for sake of brevity.

The method 600 starts, at 602, with forming a Josephson ring modulator(e.g., the JRM 106). The Josephson ring modulator can comprise one ormore Josephson junctions (e.g., the first Josephson junction 108, thesecond Josephson junction 110, the third Josephson junction 112, thefourth Josephson junction 114) arranged in a Wheatstone-bridgeconfiguration.

A superconducting surface acoustic wave resonator (e.g. thesuperconducting SAW resonator 102) can be formed, at 604. The surfaceacoustic wave resonator can be formed from a first superconducting Braggmirror (e.g., the first Bragg mirror 202) and a second superconductingBragg mirror (e.g., the second Bragg mirror 204) realized over apiezoelectric substrate. At 606, the first superconducting Bragg mirrorcan be separated from the second superconducting Bragg mirror by adistance defined as an odd integer multiple of a half-wavelength of themain mode supported by the surface acoustic wave resonator.

The method 600 can continue, at 608 and a superconducting microwaveresonator (e.g., the superconducting microwave resonator 104) can beformed. Further, at 610 of the method 600, the Josephson ring modulatorcan be coupled to the superconducting surface acoustic wave resonatorand the superconducting microwave resonator.

FIG. 7 illustrates a flow diagram of an example, non-limiting, method700 for fabrication of a device comprising a Josephson ring modulatorcoupled to a superconducting surface acoustic wave resonator and asuperconducting microwave resonator in accordance with one or moreembodiments described herein. Repetitive description of like elementsemployed in other embodiments described herein is omitted for sake ofbrevity.

At 702, a Josephson ring modulator (e.g., the JRM 106) that comprisesone or more Josephson junctions (e.g., the first Josephson junction 108,the second Josephson junction 110, the third Josephson junction 112, thefourth Josephson junction 114) can be formed. The one or more Josephsonjunctions can be arranged in a Wheatstone-bridge configuration.

A superconducting surface acoustic wave resonator (e.g., thesuperconducting SAW resonator 102) can be formed at 704 of the method700. The superconducting surface acoustic wave resonator is realized ona low-loss piezo-electric dielectric substrate. For example, thelow-loss piezo-electric dielectric substrate can comprise one or morematerials selected from a group of materials comprising one or more ofquartz, gallium arsenide, lithium niobite, and zinc oxide.

To form the superconducting surface acoustic wave resonator, at 706 ofthe method 700, an interdigitated capacitance device (e.g., the firstIDC 302) can be positioned at a center of the surface acoustic waveresonator. The interdigitated capacitance device can be positionedbetween two metallic/dielectric Bragg mirrors. For example, theinterdigitated capacitance device can be positioned between a firstBragg mirror 202 and a second Bragg mirror 204.

At 708 of the method 700, a superconducting microwave resonator (e.g.,the superconducting microwave resonator 104) can be formed. Thesuperconducting microwave resonator can be implemented usinglumped-element capacitance and/or lumped-element inductance.

Further, at 710 of the method 700, a first set of opposite nodes (e.g.,the first node 124 and the third node 128) of the Josephson ringmodulator can be coupled to opposite nodes of the interdigitatedcapacitance device. For example, one node of the first set of oppositenodes can be coupled to a first electrode of the interdigitatedcapacitance device (indicated at 304 of FIG. 3). Another node of thefirst set of opposite nodes can be coupled to a second electrode of theinterdigitated capacitance device (indicated at 306 of FIG. 3). It isnoted that, according to some implementations, coupling the Josephsonring modulator to opposite nodes of the interdigitated capacitancedevice (at 710) can occur before forming the superconducting microwaveresonator (at 708).

In addition, at 712 of the method 700, a second set of opposite nodes(e.g., the second node 126 and the fourth node 130) of the Josephsonring modulator can be coupled to one or more capacitors (e.g., the firstcapacitor 308, the second capacitor 310) of the superconductingmicrowave resonator. For example, one node of the second set of oppositenodes can be connected to a first capacitor of the superconductingmicrowave resonator. Further, the two nodes of the second set ofopposite nodes can be connected to two electrodes of the secondcapacitor of the superconducting microwave resonator.

FIG. 8 illustrates a flow diagram of an example, non-limiting, method800 for fabrication of a superconducting quantum device in accordancewith one or more embodiments described herein. Repetitive description oflike elements employed in other embodiments described herein is omittedfor sake of brevity.

A superconducting surface acoustic wave resonator (e.g., thesuperconducting SAW resonator 102) can be formed at 802 of the method800. To form the surface acoustic wave resonator, at 804 of the method,a first periodic structure (e.g., the first Bragg mirror 202) and asecond periodic structure (e.g., the second Bragg mirror 204) can beseparated by a distance defined as an odd integer multiple of ahalf-wavelength supported by the superconducting surface acoustic waveresonator. The first periodic structure can comprise first metallicfingers and first dielectric gaps in between the metallic fingers. Thesecond periodic structure can comprise second metallic fingers andsecond dielectric gaps in between the metallic fingers.

At 806 of the method 800, a superconducting microwave resonator (e.g.,the superconducting microwave resonator 104) can be formed. Thesuperconducting microwave resonator can comprise one or more capacitors(e.g., the first capacitor 308 and the second capacitor 310). Onecapacitor of the one or more capacitors can be a shunting capacitor forthe JRM.

Further, a Josephson ring modulator (e.g., the JRM 106) can be coupledto the surface acoustic wave resonator, at 808 of the method. At 810 ofthe method 800, the superconducting microwave resonator can be coupledto the Josephson ring modulator. According to some implementations, theJosephson ring modulator can comprise one or more Josephson junctions(e.g., the first Josephson junction 108, the second Josephson junction110, the third Josephson junction 112, the fourth Josephson junction114) arranged in a Wheatstone-bridge configuration. In someimplementations, the Josephson ring modulator can be a dispersivenonlinear three-wave mixing element. It is noted that, according to someimplementations, coupling the Josephson ring modulator to the surfaceacoustic wave resonator (at 810) can occur before forming thesuperconducting microwave resonator (at 808).

According to some implementations, an interdigitated capacitance devicecan be positioned at a center of the surface acoustic wave resonator.Further to these implementations, a first set of opposite nodes of theJosephson ring modulator can be connected to opposite nodes of theinterdigitated capacitance device. In some implementations, the methodcan include inducing magnetic flux threading the Josephson ringmodulator.

FIG. 9 illustrates a flow diagram of an example, non-limiting, method900 for fabrication of a superconducting quantum device comprisingexternal feedlines in accordance with one or more embodiments describedherein. Repetitive description of like elements employed in otherembodiments described herein is omitted for sake of brevity.

At 902 of the method 900, a Josephson ring modulator (e.g., the JRM 106)can be formed. The Josephson ring modulator can comprise one or moreJosephson junctions (e.g., the first Josephson junction 108, the secondJosephson junction 110, the third Josephson junction 112, the fourthJosephson junction 114). The one or more Josephson junctions can bearranged in a Wheatstone-bridge configuration. According to someimplementations, the Josephson ring modulator can be a dispersivenonlinear three-wave mixing element.

At 904 of the method 900, the Josephson ring modulator can be coupled toa superconducting surface acoustic wave resonator (e.g., thesuperconducting SAW resonator 102) and a superconducting microwaveresonator (e.g., the superconducting microwave resonator 104).

A first external feedline (e.g., the first external feedline 210) can becoupled to the surface acoustic wave resonator, at 906 of the method900. For example, the first external feedline can be coupled to thesurface acoustic wave resonator through another interdigitatedcapacitance device. The first external feedline can carry one or morefirst input signals and one or more first output signals of the surfaceacoustic wave resonator.

Further, at 908 of the method 900, a second external feedline (e.g., thesecond external feedline 214) can be coupled to the superconductingmicrowave resonator. The second external feedline can carry one or moresecond input signals and one or more second output signals of thesuperconducting microwave resonator.

In an example, one superconducting SAW resonator (low-frequency) and onesuperconducting microwave resonator (high-frequency) can be coupled tothe JRM. The superconducting SAW resonator can comprise twosuperconducting Bragg mirrors separated from one another by a distancethat is an odd integer multiple of half-wavelength of the main modesupported by the superconducting SAW resonator. The superconducting SAWresonator can be realized on a low-loss piezo-electric dielectricsubstrate. Further, the JRM can be realized using Al or Nb Josephsonjunctions.

One pair of opposite nodes of the JRM can be connected to opposite nodesof the IDC. The IDC can be positioned off-center of the SAW resonator(e.g., at a location that does not coincide with a voltage node of thedesired coupled mode). The other pair of opposite nodes of the JRM canbe connected to a shunt capacitor and, optionally, a shunt inductor. Themicrowave resonator can be coupled to an external feedline through acoupling capacitor. The external feedline can carry the input and outputsignals of the microwave resonator. The superconducting SAW resonatorcan have a separate external feedline which can carry the input andoutput signals of the SAW resonator. The external feedline can becoupled to the SAW resonator using a designated IDC. The IDC fingers canbe located close to rf-voltage antinodes. A pump drive can be injectedto the JRM using a separate port. The pump port can be connected to thesigma port of a 180-degree hybrid, which in turn could be capacitivelycoupled to opposite nodes of the JRM (giving rise to a common excitationof the JRM).

For simplicity of explanation, the methodologies and/orcomputer-implemented methodologies are depicted and described as aseries of acts. It is to be understood and appreciated that the subjectinnovation is not limited by the acts illustrated and/or by the order ofacts, for example acts can occur in various orders and/or concurrently,and with other acts not presented and described herein. Furthermore, notall illustrated acts can be required to implement thecomputer-implemented methodologies in accordance with the disclosedsubject matter. In addition, those skilled in the art will understandand appreciate that the computer-implemented methodologies couldalternatively be represented as a series of interrelated states via astate diagram or events. Additionally, it should be further appreciatedthat the computer-implemented methodologies disclosed hereinafter andthroughout this specification are capable of being stored on an articleof manufacture to facilitate transporting and transferring suchcomputer-implemented methodologies to computers. The term article ofmanufacture, as used herein, is intended to encompass a computer programaccessible from any computer-readable device or storage media.

In order to provide a context for the various aspects of the disclosedsubject matter, FIG. 10 as well as the following discussion are intendedto provide a general description of a suitable environment in which thevarious aspects of the disclosed subject matter can be implemented. FIG.10 illustrates a block diagram of an example, non-limiting operatingenvironment in which one or more embodiments described herein can befacilitated. Repetitive description of like elements employed in otherembodiments described herein is omitted for sake of brevity. Withreference to FIG. 10, a suitable operating environment 1000 forimplementing various aspects of this disclosure can also include acomputer 1012. The computer 1012 can also include a processing unit1014, a system memory 1016, and a system bus 1018. The system bus 1018couples system components including, but not limited to, the systemmemory 1016 to the processing unit 1014. The processing unit 1014 can beany of various available processors. Dual microprocessors and othermultiprocessor architectures also can be employed as the processing unit1014. The system bus 1018 can be any of several types of busstructure(s) including the memory bus or memory controller, a peripheralbus or external bus, and/or a local bus using any variety of availablebus architectures including, but not limited to, Industrial StandardArchitecture (ISA), Micro-Channel Architecture (MSA), Extended ISA(EISA), Intelligent Drive Electronics (IDE), VESA Local Bus (VLB),Peripheral Component Interconnect (PCI), Card Bus, Universal Serial Bus(USB), Advanced Graphics Port (AGP), Firewire (IEEE 1394), and SmallComputer Systems Interface (SCSI). The system memory 1016 can alsoinclude volatile memory 1020 and nonvolatile memory 1022. The basicinput/output system (BIOS), containing the basic routines to transferinformation between elements within the computer 1012, such as duringstart-up, is stored in nonvolatile memory 1022. By way of illustration,and not limitation, nonvolatile memory 1022 can include read only memory(ROM), programmable ROM (PROM), electrically programmable ROM (EPROM),electrically erasable programmable ROM (EEPROM), flash memory, ornonvolatile random access memory (RAM) (e.g., ferroelectric RAM(FeRAM)). Volatile memory 1020 can also include random access memory(RAM), which acts as external cache memory. By way of illustration andnot limitation, RAM is available in many forms such as static RAM(SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rateSDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM),direct Rambus RAM (DRRAM), direct Rambus dynamic RAM (DRDRAM), andRambus dynamic RAM.

Computer 1012 can also include removable/non-removable,volatile/non-volatile computer storage media. FIG. 10 illustrates, forexample, a disk storage 1024. Disk storage 1024 can also include, but isnot limited to, devices like a magnetic disk drive, floppy disk drive,tape drive, Jaz drive, Zip drive, LS-100 drive, flash memory card, ormemory stick. The disk storage 1024 also can include storage mediaseparately or in combination with other storage media including, but notlimited to, an optical disk drive such as a compact disk ROM device(CD-ROM), CD recordable drive (CD-R Drive), CD rewritable drive (CD-RWDrive) or a digital versatile disk ROM drive (DVD-ROM). To facilitateconnection of the disk storage 1024 to the system bus 1018, a removableor non-removable interface is typically used, such as interface 1026.FIG. 10 also depicts software that acts as an intermediary between usersand the basic computer resources described in the suitable operatingenvironment 1000. Such software can also include, for example, anoperating system 1028. Operating system 1028, which can be stored ondisk storage 1024, acts to control and allocate resources of thecomputer 1012. System applications 1030 take advantage of the managementof resources by operating system 1028 through program modules 1032 andprogram data 1034, e.g., stored either in system memory 1016 or on diskstorage 1024. It is to be appreciated that this disclosure can beimplemented with various operating systems or combinations of operatingsystems. A user enters commands or information into the computer 1012through input device(s) 1036. Input devices 1036 include, but are notlimited to, a pointing device such as a mouse, trackball, stylus, touchpad, keyboard, microphone, joystick, game pad, satellite dish, scanner,TV tuner card, digital camera, digital video camera, web camera, and thelike. These and other input devices connect to the processing unit 1014through the system bus 1018 via interface port(s) 1038. Interfaceport(s) 1038 include, for example, a serial port, a parallel port, agame port, and a universal serial bus (USB). Output device(s) 1040 usesome of the same type of ports as input device(s) 1036. Thus, forexample, a USB port can be used to provide input to computer 1012, andto output information from computer 1012 to an output device 1040.Output adapter 1042 is provided to illustrate that there are some outputdevices 1040 like monitors, speakers, and printers, among other outputdevices 1040, which require special adapters. The output adapters 1042include, by way of illustration and not limitation, video and soundcards that provide a method of connection between the output device 1040and the system bus 1018. It should be noted that other devices and/orsystems of devices provide both input and output capabilities such asremote computer(s) 1044.

Computer 1012 can operate in a networked environment using logicalconnections to one or more remote computers, such as remote computer(s)1044. The remote computer(s) 1044 can be a computer, a server, a router,a network PC, a workstation, a microprocessor based appliance, a peerdevice or other common network node and the like, and typically can alsoinclude many or all of the elements described relative to computer 1012.For purposes of brevity, only a memory storage device 1046 isillustrated with remote computer(s) 1044. Remote computer(s) 1044 islogically connected to computer 1012 through a network interface 1048and then physically connected via communication connection 1050. Networkinterface 1048 encompasses wire and/or wireless communication networkssuch as local-area networks (LAN), wide-area networks (WAN), cellularnetworks, etc. LAN technologies include Fiber Distributed Data Interface(FDDI), Copper Distributed Data Interface (CDDI), Ethernet, Token Ringand the like. WAN technologies include, but are not limited to,point-to-point links, circuit switching networks like IntegratedServices Digital Networks (ISDN) and variations thereon, packetswitching networks, and Digital Subscriber Lines (DSL). Communicationconnection(s) 1050 refers to the hardware/software employed to connectthe network interface 1048 to the system bus 1018. While communicationconnection 1050 is shown for illustrative clarity inside computer 1012,it can also be external to computer 1012. The hardware/software forconnection to the network interface 1048 can also include, for exemplarypurposes only, internal and external technologies such as, modemsincluding regular telephone grade modems, cable modems and DSL modems,ISDN adapters, and Ethernet cards.

The present invention may be a system, a method, an apparatus and/or acomputer program product at any possible technical detail level ofintegration. The computer program product can include a computerreadable storage medium (or media) having computer readable programinstructions thereon for causing a processor to carry out aspects of thepresent invention. The computer readable storage medium can be atangible device that can retain and store instructions for use by aninstruction execution device. The computer readable storage medium canbe, for example, but is not limited to, an electronic storage device, amagnetic storage device, an optical storage device, an electromagneticstorage device, a semiconductor storage device, or any suitablecombination of the foregoing. A non-exhaustive list of more specificexamples of the computer readable storage medium can also include thefollowing: a portable computer diskette, a hard disk, a random accessmemory (RAM), a read-only memory (ROM), an erasable programmableread-only memory (EPROM or Flash memory), a static random access memory(SRAM), a portable compact disc read-only memory (CD-ROM), a digitalversatile disk (DVD), a memory stick, a floppy disk, a mechanicallyencoded device such as punch-cards or raised structures in a groovehaving instructions recorded thereon, and any suitable combination ofthe foregoing. A computer readable storage medium, as used herein, isnot to be construed as being transitory signals per se, such as radiowaves or other freely propagating electromagnetic waves, electromagneticwaves propagating through a waveguide or other transmission media (e.g.,light pulses passing through a fiber-optic cable), or electrical signalstransmitted through a wire.

Computer readable program instructions described herein can bedownloaded to respective computing/processing devices from a computerreadable storage medium or to an external computer or external storagedevice via a network, for example, the Internet, a local area network, awide area network and/or a wireless network. The network can comprisecopper transmission cables, optical transmission fibers, wirelesstransmission, routers, firewalls, switches, gateway computers and/oredge servers. A network adapter card or network interface in eachcomputing/processing device receives computer readable programinstructions from the network and forwards the computer readable programinstructions for storage in a computer readable storage medium withinthe respective computing/processing device. Computer readable programinstructions for carrying out operations of the present invention can beassembler instructions, instruction-set-architecture (ISA) instructions,machine instructions, machine dependent instructions, microcode,firmware instructions, state-setting data, configuration data forintegrated circuitry, or either source code or object code written inany combination of one or more programming languages, including anobject oriented programming language such as Smalltalk, C++, or thelike, and procedural programming languages, such as the “C” programminglanguage or similar programming languages. The computer readable programinstructions can execute entirely on the user's computer, partly on theuser's computer, as a stand-alone software package, partly on the user'scomputer and partly on a remote computer or entirely on the remotecomputer or server. In the latter scenario, the remote computer can beconnected to the user's computer through any type of network, includinga local area network (LAN) or a wide area network (WAN), or theconnection can be made to an external computer (for example, through theInternet using an Internet Service Provider). In some embodiments,electronic circuitry including, for example, programmable logiccircuitry, field-programmable gate arrays (FPGA), or programmable logicarrays (PLA) can execute the computer readable program instructions byutilizing state information of the computer readable programinstructions to personalize the electronic circuitry, in order toperform aspects of the present invention.

Aspects of the present invention are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer readable program instructions. These computer readable programinstructions can be provided to a processor of a general purposecomputer, special purpose computer, or other programmable dataprocessing apparatus to produce a machine, such that the instructions,which execute via the processor of the computer or other programmabledata processing apparatus, create method for implementing thefunctions/acts specified in the flowchart and/or block diagram block orblocks. These computer readable program instructions can also be storedin a computer readable storage medium that can direct a computer, aprogrammable data processing apparatus, and/or other devices to functionin a particular manner, such that the computer readable storage mediumhaving instructions stored therein comprises an article of manufactureincluding instructions which implement aspects of the function/actspecified in the flowchart and/or block diagram block or blocks. Thecomputer readable program instructions can also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational acts to be performed on the computer,other programmable apparatus or other device to produce a computerimplemented process, such that the instructions which execute on thecomputer, other programmable apparatus, or other device implement thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams can represent a module, segment, or portionof instructions, which comprises one or more executable instructions forimplementing the specified logical function(s). In some alternativeimplementations, the functions noted in the blocks can occur out of theorder noted in the Figures. For example, two blocks shown in successioncan, in fact, be executed substantially concurrently, or the blocks cansometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

While the subject matter has been described above in the general contextof computer-executable instructions of a computer program product thatruns on a computer and/or computers, those skilled in the art willrecognize that this disclosure also can be implemented in combinationwith other program modules. Generally, program modules include routines,programs, components, data structures, etc. that perform particulartasks and/or implement particular abstract data types. Moreover, thoseskilled in the art will appreciate that the inventivecomputer-implemented methods can be practiced with other computer systemconfigurations, including single-processor or multiprocessor computersystems, mini-computing devices, mainframe computers, as well ascomputers, hand-held computing devices (e.g., PDA, phone),microprocessor-based or programmable consumer or industrial electronics,and the like. The illustrated aspects can also be practiced indistributed computing environments where tasks are performed by remoteprocessing devices that are linked through a communications network.However, some, if not all aspects of this disclosure can be practiced onstand-alone computers. In a distributed computing environment, programmodules can be located in both local and remote memory storage devices.

As used in this application, the terms “component,” “system,”“platform,” “interface,” and the like, can refer to and/or can include acomputer-related entity or an entity related to an operational machinewith one or more specific functionalities. The entities disclosed hereincan be either hardware, a combination of hardware and software,software, or software in execution. For example, a component can be, butis not limited to being, a process running on a processor, a processor,an object, an executable, a thread of execution, a program, and/or acomputer. By way of illustration, both an application running on aserver and the server can be a component. One or more components canreside within a process and/or thread of execution and a component canbe localized on one computer and/or distributed between two or morecomputers. In another example, respective components can execute fromvarious computer readable media having various data structures storedthereon. The components can communicate via local and/or remoteprocesses such as in accordance with a signal having one or more datapackets (e.g., data from one component interacting with anothercomponent in a local system, distributed system, and/or across a networksuch as the Internet with other systems via the signal). As anotherexample, a component can be an apparatus with specific functionalityprovided by mechanical parts operated by electric or electroniccircuitry, which is operated by a software or firmware applicationexecuted by a processor. In such a case, the processor can be internalor external to the apparatus and can execute at least a part of thesoftware or firmware application. As yet another example, a componentcan be an apparatus that provides specific functionality throughelectronic components without mechanical parts, wherein the electroniccomponents can include a processor or other method to execute softwareor firmware that confers at least in part the functionality of theelectronic components. In an aspect, a component can emulate anelectronic component via a virtual machine, e.g., within a cloudcomputing system.

In addition, the term “or” is intended to mean an inclusive “or” ratherthan an exclusive “or.” That is, unless specified otherwise, or clearfrom context, “X employs A or B” is intended to mean any of the naturalinclusive permutations. That is, if X employs A; X employs B; or Xemploys both A and B, then “X employs A or B” is satisfied under any ofthe foregoing instances. Moreover, articles “a” and “an” as used in thesubject specification and annexed drawings should generally be construedto mean “one or more” unless specified otherwise or clear from contextto be directed to a singular form. As used herein, the terms “example”and/or “exemplary” are utilized to mean serving as an example, instance,or illustration. For the avoidance of doubt, the subject matterdisclosed herein is not limited by such examples. In addition, anyaspect or design described herein as an “example” and/or “exemplary” isnot necessarily to be construed as preferred or advantageous over otheraspects or designs, nor is it meant to preclude equivalent exemplarystructures and techniques known to those of ordinary skill in the art.

As it is employed in the subject specification, the term “processor” canrefer to substantially any computing processing unit or devicecomprising, but not limited to, single-core processors;single-processors with software multithread execution capability;multi-core processors; multi-core processors with software multithreadexecution capability; multi-core processors with hardware multithreadtechnology; parallel platforms; and parallel platforms with distributedshared memory. Additionally, a processor can refer to an integratedcircuit, an application specific integrated circuit (ASIC), a digitalsignal processor (DSP), a field programmable gate array (FPGA), aprogrammable logic controller (PLC), a complex programmable logic device(CPLD), a discrete gate or transistor logic, discrete hardwarecomponents, or any combination thereof designed to perform the functionsdescribed herein. Further, processors can exploit nano-scalearchitectures such as, but not limited to, molecular and quantum-dotbased transistors, switches and gates, in order to optimize space usageor enhance performance of user equipment. A processor can also beimplemented as a combination of computing processing units. In thisdisclosure, terms such as “store,” “storage,” “data store,” datastorage,” “database,” and substantially any other information storagecomponent relevant to operation and functionality of a component areutilized to refer to “memory components,” entities embodied in a“memory,” or components comprising a memory. It is to be appreciatedthat memory and/or memory components described herein can be eithervolatile memory or nonvolatile memory, or can include both volatile andnonvolatile memory. By way of illustration, and not limitation,nonvolatile memory can include read only memory (ROM), programmable ROM(PROM), electrically programmable ROM (EPROM), electrically erasable ROM(EEPROM), flash memory, or nonvolatile random access memory (RAM) (e.g.,ferroelectric RAM (FeRAM). Volatile memory can include RAM, which canact as external cache memory, for example. By way of illustration andnot limitation, RAM is available in many forms such as synchronous RAM(SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rateSDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM),direct Rambus RAM (DRRAM), direct Rambus dynamic RAM (DRDRAM), andRambus dynamic RAM (RDRAM). Additionally, the disclosed memorycomponents of systems or computer-implemented methods herein areintended to include, without being limited to including, these and anyother suitable types of memory.

What has been described above include mere examples of systems andcomputer-implemented methods. It is, of course, not possible to describeevery conceivable combination of components or computer-implementedmethods for purposes of describing this disclosure, but one of ordinaryskill in the art can recognize that many further combinations andpermutations of this disclosure are possible. Furthermore, to the extentthat the terms “includes,” “has,” “possesses,” and the like are used inthe detailed description, claims, appendices and drawings such terms areintended to be inclusive in a manner similar to the term “comprising” as“comprising” is interpreted when employed as a transitional word in aclaim. The descriptions of the various embodiments have been presentedfor purposes of illustration, but are not intended to be exhaustive orlimited to the embodiments disclosed. Many modifications and variationswill be apparent to those of ordinary skill in the art without departingfrom the scope and spirit of the described embodiments. The terminologyused herein was chosen to best explain the principles of theembodiments, the practical application or technical improvement overtechnologies found in the marketplace, or to enable others of ordinaryskill in the art to understand the embodiments disclosed herein.

What is claimed is:
 1. A superconducting device, comprising: asuperconducting surface acoustic wave resonator; a superconductingmicrowave resonator; and a Josephson ring modulator coupled to thesuperconducting surface acoustic wave resonator and the superconductingmicrowave resonator, wherein the Josephson ring modulator is adispersive nonlinear three-wave mixing element.
 2. The superconductingdevice of claim 1, wherein the superconducting surface acoustic waveresonator comprises: a first superconducting Bragg mirror; and a secondsuperconducting Bragg mirror separated from the first superconductingBragg mirror by a distance that is an odd integer multiple of ahalf-wavelength supported by the superconducting surface acoustic waveresonator.
 3. The superconducting device of claim 1, wherein thesuperconducting surface acoustic wave resonator is realized on alow-loss piezo-electric dielectric substrate that comprises a materialselected from a group of materials consisting of quartz, galliumarsenide, lithium niobite, and zinc oxide.
 4. The superconducting deviceof claim 1, wherein the Josephson ring modulator comprises one or moreJosephson junctions arranged in a Wheatstone-bridge configuration, andwherein the one or more Josephson junctions comprise a material selectedfrom a group of materials consisting of aluminum and niobium.
 5. Thesuperconducting device of claim 1, further comprising: an interdigitatedcapacitance device positioned at a center of the superconducting surfaceacoustic wave resonator, wherein a first set of opposite nodes of theJosephson ring modulator are connected to opposite nodes of theinterdigitated capacitance device.
 6. The superconducting device ofclaim 5, wherein a second set of opposite nodes of the Josephson ringmodulator are connected to a shunt capacitor.
 7. The superconductingdevice of claim 1, further comprising: a first external feedline coupledto the superconducting surface acoustic wave resonator through aninterdigitated capacitance device, wherein the first external feedlinecarries one or more first input signals and one or more first outputsignals of the superconducting surface acoustic wave resonator; and asecond external feedline coupled to the superconducting microwaveresonator, wherein the second external feedline carries one or moresecond input signals and one or more second output signals of thesuperconducting microwave resonator.
 8. The superconducting device ofclaim 1, wherein induced magnetic flux threads the Josephson ringmodulator.
 9. The superconducting device of claim 1, wherein theJosephson ring modulator comprises a port, wherein a pump drive isinjected to the Josephson ring modulator through the port.
 10. Asuperconducting circuit, comprising: a superconducting surface acousticwave resonator; a Josephson ring modulator coupled to thesuperconducting surface acoustic wave resonator; and a superconductingmicrowave resonator coupled to the Josephson ring modulator, wherein theJosephson ring modulator is a dispersive nonlinear three-wave mixingelement, and wherein the superconducting surface acoustic wave resonatoris realized on a low-loss piezo-electric dielectric substrate.
 11. Thesuperconducting circuit of claim 10, wherein the superconducting surfaceacoustic wave resonator comprises: a first superconducting Bragg mirrorand a second superconducting Bragg mirror separated by a distance thatis an odd integer multiple of a half-wavelength supported by thesuperconducting surface acoustic wave resonator.
 12. The superconductingcircuit of claim 10, wherein the Josephson ring modulator comprises oneor more Josephson junctions that comprise a material selected from agroup of materials consisting of aluminum and niobium.
 13. Thesuperconducting circuit of claim 10, further comprising: aninterdigitated capacitance device positioned at a center of thesuperconducting surface acoustic wave resonator, wherein a first set ofopposite nodes of the Josephson ring modulator are connected to oppositenodes of the interdigitated capacitance device, and wherein a second setof opposite nodes of the Josephson ring modulator are connected to ashunt capacitor, wherein the interdigitated capacitance device, theshunt capacitor, and the Josephson ring modulator form thesuperconducting microwave resonator.
 14. The superconducting circuit ofclaim 10, further comprising: a first external feedline coupled to thesuperconducting surface acoustic wave resonator through aninterdigitated capacitance device, wherein the first external feedlinecarries one or more first input signals and one or more first outputsignals of the superconducting surface acoustic wave resonator; and asecond external feedline coupled to the superconducting microwaveresonator, wherein the second external feedline carries one or moresecond input signals and one or more second output signals of thesuperconducting microwave resonator.
 15. A method, comprising: forming aJosephson ring modulator that comprises one or more Josephson junctionsarranged in a Wheatstone-bridge configuration; and coupling theJosephson ring modulator to a superconducting surface acoustic waveresonator and a superconducting microwave resonator, wherein theJosephson ring modulator is a dispersive nonlinear three-wave mixingelement.
 16. The method of claim 15, further comprising: forming thesuperconducting surface acoustic wave resonator from a firstsuperconducting Bragg mirror and a second superconducting Bragg mirror;and separating the first superconducting Bragg mirror from the secondsuperconducting Bragg mirror by a distance defined as an odd integermultiple of a half-wavelength supported by the superconducting surfaceacoustic wave resonator.
 17. The method of claim 15, wherein the one ormore Josephson junctions comprise a first material selected from a firstgroup of materials consisting of aluminum and niobium, the methodfurther comprising: realizing the superconducting surface acoustic waveresonator on a low-loss piezo-electric dielectric substrate, wherein thelow-loss piezo-electric dielectric substrate comprises a second materialselected from a second group of materials consisting of quartz, galliumarsenide, lithium niobite, and zinc oxide.
 18. The method of claim 15,further comprising: positioning an interdigitated capacitance device ata center of the superconducting surface acoustic wave resonator;connecting a first set of opposite nodes of the Josephson ring modulatorto opposite nodes of the interdigitated capacitance device; andconnecting a second set of opposite nodes of the Josephson ringmodulator to one or more capacitors of the superconducting microwaveresonator.
 19. The method of claim 15, further comprising: inducingmagnetic flux threading the Josephson ring modulator.